Consider the matrix A=(1000cosθ−sinθ0sinθcosθ)A = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos\theta & -\sin\theta \\ 0 & \sin\theta & \cos\theta \end{pmatrix}A=1000cosθsinθ0−sinθcosθ. Which of the following is equal to det(An)\det(A^n)det(An) for any integer n≥1n \geq 1n≥1?
111
cos(nθ)\cos(n\theta)cos(nθ)
(−1)n(-1)^n(−1)n
000